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Nonhomogeneous Dirichlet problems without the Ambrosetti-Rabinowitz condition
ID Li, Gang (Avtor), ID Rǎdulescu, Vicenţiu (Avtor), ID Repovš, Dušan (Avtor), ID Zhang, Qihu (Avtor)

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Izvleček
We consider the existence of solutions of the following ▫$p(x)$▫-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition: ▫$$ \begin{cases} -\text{div} \, (|\nabla u|^{p(x)-2}\nabla u) = f(x,u) & \text{ in } \quad \Omega , \\ u=0 & \text{ on } \quad \partial \Omega . \end{cases} $$▫ We give a new growth condition and we point out its importance for checking the Cerami compactness condition. We prove the existence of solutions of the above problem via the critical point theory, and also provide some multiplicity properties. The present paper extend previous results of Q. Zhang and C. Zhao (Existence of strong solutions of a ▫$p(x)$▫-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition, Computers and Mathematics with Applications, 2015) and we establish the existence of solutions under weaker hypotheses on the nonlinear term.

Jezik:Angleški jezik
Ključne besede:nonhomogeneous differential operator, Ambrosetti-Rabinowitz condition, Cerami compactness condition, Sobolev space with variable exponent
Vrsta gradiva:Članek v reviji (dk_c)
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:PEF - Pedagoška fakulteta
FMF - Fakulteta za matematiko in fiziko
Leto izida:2018
Št. strani:Str. 55-77
Številčenje:Vol. 51, no. 1
UDK:517.956.2
ISSN pri članku:1230-3429
DOI:10.12775/TMNA.2017.037 Povezava se odpre v novem oknu
COBISS.SI-ID:18162521 Povezava se odpre v novem oknu
Datum objave v RUL:29.08.2019
Število ogledov:541
Število prenosov:370
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Gradivo je del revije

Naslov:Topological Methods in Nonlinear Analysis
Skrajšan naslov:Topol. Methods Nonlinear Anal.
Založnik:Juliusz Schauder Center
ISSN:1230-3429
COBISS.SI-ID:14203653 Povezava se odpre v novem oknu

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